Fill a large stock pot with water and bring to a rolling boil; add a pinch of salt if desired.
Add the penne and cook for about 9 minutes until al dente.
With the pasta boiling, add the frozen chopped broccoli and cook 2–4 minutes until heated and tender.
Drain the pasta and broccoli together in a colander and set aside.
In a large skillet, combine the cubed chicken, oil and 2–3 tablespoons Cajun seasoning; mix to coat evenly.
Cook the seasoned chicken over medium-high heat until cooked through and no longer pink, about 6–8 minutes depending on size; remove from skillet and keep warm.
Reduce heat to medium-low and add butter to the same skillet; stir in minced garlic and cook briefly until fragrant, about 30 seconds.
Whisk in the chicken broth, heavy cream and flour; cook over medium-low, whisking constantly until the sauce thickens and begins to bubble.
Return the cooked chicken to the skillet, then add the drained pasta and broccoli; toss gently to coat everything in the sauce.
Sprinkle with shredded Parmesan, stir briefly to combine, then serve hot.
